Fiber Orientation State Research Articles

Efficient Approximation of Varying Fiber Orientation States in Injection Molded Parts Under Consideration of Multiple Manufacturing Uncertainties

AbstractThe production of high-quality fiber reinforced polymer parts is an important aspect in several industrial areas. However, due to unavoidable uncertainties in material and manufacturing processes, the part quality scatters. One important aspect here is the fiber orientation, being crucial for the thermo-mechanical properties of the part and being influenced by the uncertain material state and process conditions. Process simulations are an important tool for predicting the fiber orientation, but state-of-the-art simulations are normally deterministic and represent only one specific case. Performing enough deterministic simulations to model manufacturing uncertainties requires high numerical effort. Therefore, this work presents methods to quickly and efficiently approximate the fiber orientation under varying material and process parameters, requiring only a few simulations as input. Different schemes for approximation are evaluated and compared with each other and with 3D process simulations.

The use of digital thread for reconstruction of local fiber orientation in a compression molded pin bracket via deep learning

A deep convolutional neural network (DCNN) was used for microstructure reconstruction using artificial intelligence (MR-AI) by predicting local average fiber orientation distributions (FOD) in a 3D prepreg platelet molded composite (PPMC) pin bracket. To train the MR-AI model, surface strain fields from residual stresses simulated in PPMC plates were used as the input to the DCNN. A training dataset included PPMC plates with various degrees of global fiber alignment, based on the information obtained from high-fidelity flow simulation of a pin bracket. The MR-AI model was then deployed to analyze FOD in the 3D pin bracket by conducting thermo-elastic residual stress analysis. Initially, the MR-AI model was established entirely on the synthetic simulation data. Then, a μCT scan of a physically molded pin bracket was used to create a finite element model that provided data for additional validation of the DCNN model. For the μCT scan finite element pin bracket the MR-AI model predicted the distribution of fiber orientation tensor components with MAE of 0.10 indicating a global prediction error of 10 %. For the flow simulated pin bracket, the MR-AI model predicted the distribution of fiber orientation tensor components with a global prediction error of 11 %. The MR-AI model showed the ability to predict regions of varying alignment in the base and flange of the pin bracket. The proposed MR-AI methodology allows for rapid prediction of FOD in geometrically complex parts and offers a promising path to detecting unique fiber orientation states in molded components.

Influence of Flow-Induced Polymorphism and Fiber Morphology on Mechanical Behavior in Long Discontinuous Glass Fiber Polyamide Composites

This study investigates the combined flow-induced crystallization in the polymer and fiber reorientation during compression molding of a long discontinuous glass fiber polyamide (PA 6) composite. The composite is molded from an organosheet (a semi-finished pre-impregnated mat); the composite anisotropic tensile properties are evaluated as a function of polymer crystalline morphology and fiber orientation state, both controlled by the extent of material flow in the mold. To study these effects, the full mold coverage and partial center charge of organosheet (OS)-80 %, 60 %, 50 %, and 40 % were compression molded to cause varying anisotropic material flow. Tensile specimens were cut out from the molded plates in the flow and transverse direction and tested to compare their effective tensile properties (modulus and strength). The flow-induced morphological changes in a molded composite at the glass fiber bundle microstructure scale and polymer crystalline phases nano-structure were characterized using optical microscopy and X-ray diffraction, respectively. These morphological changes contributed to the significant change in the tensile strength and modulus; a combined experimental/numerical simulation framework was used to segregate the relative contribution of each factor. Experimentally, the tensile modulus increased in the flow direction from 9.6GPa to 14.9GPa for the specimens produced by full mold coverage and OS-50 % coverage mold, respectively. The tensile strength increased from 162 MPa to 254 MPa for the full and OS-60 % mold coverage. On the contrary, the strength and modulus in the transverse direction to the flow showed a significant drop to 35 MPa and 3GPa, respectively, which was attributed to reduced fiber alignment and anisotropy in the PA6 matrix.

Machine learning assisted discovery of effective viscous material laws for shear-thinning fiber suspensions

AbstractIn this article, we combine a Fast Fourier Transform based computational approach and a supervised machine learning strategy to discover models for the anisotropic effective viscosity of shear-thinning fiber suspensions. Using the Fast Fourier Transform based computational approach, we study the effects of the fiber orientation state and the imposed macroscopic shear rate tensor on the effective viscosity for a broad range of shear rates of engineering process interest. We visualize the effective viscosity in three dimensions and find that the anisotropy of the effective viscosity and its shear rate dependence vary strongly with the fiber orientation state. Combining the results of this work with insights from literature, we formulate four requirements a model of the effective viscosity should satisfy for shear-thinning fiber suspensions with a Cross-type matrix fluid. Furthermore, we introduce four model candidates with differing numbers of parameters and different theoretical motivations, and use supervised machine learning techniques for non-convex optimization to identify parameter sets for the model candidates. By doing so, we leverage the flexibility of automatic differentiation and the robustness of gradient based, supervised machine learning. Finally, we identify the most suitable model by comparing the prediction accuracy of the model candidates on the fiber orientation triangle, and find that multiple models predict the anisotropic shear-thinning behavior to engineering accuracy over a broad range of shear rates.

Recognition of local fiber orientation state in prepreg platelet molded composites via deep learning

This paper presents a novel deep learning approach for reconstruction of local through-the-thickness fiber orientation distribution (FOD) in discontinuous long-fiber, prepreg-platelet molded composites (PPMC). The thermal-residual strains on composite surfaces are used as inputs to train a fully convolutional neural network, named U-Net, to predict spatially varying, local FOD. High fidelity synthetic data was generated via computational simulation of PPMC with stochastic material orientation state and was used for training the deep learning model. The proposed U-Net model allowed for rapid recognition of PPMC morphology by solving the inverse structural mechanics problem of determining the average fiber orientation through the composite thickness based on the provided surface strain measurements. Upon training and validation, the U-Net deep learning model was deployed to rapidly predict complex distributions of the local through-the-thickness FOD in PPMC.

Fiber reorientation due to obstacles in open channel flow

A model along with experimental validation is presented for fiber re-orientation within the flow of a thin fluid layer down an inclined plane. Unlike the usual approach (Jeffery), the model accommodates the fast-changing velocity gradient defying linearization and the flow constraints due to the thin thickness of the fluid film. Model equations are formulated, and the algorithm for the fiber rotation is developed. The velocity field within the channel is obtained, using COMSOLTM multiphase simulation. The formulated model equations are used to track the orientation of a single fiber. The spatial fiber orientation state is described in terms of the second order tensor by tracking multiple individual fibers with different initial orientations. To validate the model's predictions, an experimental setup was fabricated to record individual fiber kinematics during the flow and to describe the orientation of fibers in the open channel. A novel benchmark for assessing fiber re-orientation models is presented, wherein the dynamics of fiber orientation is observed in response to a semicircular obstacle within the fluid flow. The experimental results are compared to model predictions and are in reasonable agreement. Despite the simplified approach, both the dynamic of single fiber and the development of fiber orientation distribution due to the obstacle can be reasonably predicted.

Experimental Validation of Reconstructed Microstructure via Deep Learning in Discontinuous Fiber Platelet Composite

Abstract A novel approach for microstructure reconstruction using artificial intelligence (MR-AI) was proposed to nondestructively measure the through-thickness average stochastic fiber orientation distribution (FOD) in a prepreg platelet molded composite (PPMC) plate. MR-AI approach uses thermal strain components on the surfaces of a PPMC plate as input to the deep learning model, which allows to predict a distribution of local through-thickness average fiber orientation state in the entire PPMC volume. The experimental setup with a heating stage and digital image correlation (DIC) was used to measure thermal strains on the surface of the PPMC plate. Optical microscopy was then used to measure FOD in the cross section of the PPMC plate. FOD measurements from optical microscopy imagery compared favorably with FOD prediction by MR-AI. The proposed methodology opens the opportunity for rapid, nondestructive inspection of manufacturing-induced FOD in molded composites.

Three‐dimensional polymer composite flow simulation and associated fiber orientation prediction for large area extrusion deposition additive manufacturing

AbstractMaterial flow and associated fiber orientation are among the most important features in Large Area extrusion deposition Additive Manufacturing (LAAM) of short fiber‐filled composites. Endeavors have been done in 2D flow models, where significant knowledge is achieved in explaining the material anisotropy of the deposited composite parts. Nevertheless, 2D flow models are limited by a couple of assumptions that lose significant characters of the deposition flow. This study is one of the first few that employ a 3D flow model which focuses on the quasi‐steady state of the polymer composite melt flow within the nozzle and the subsequent 90‐degree turning deposition onto the material substrate. The material flow is assumed as a highly viscous Newtonian flow. The fiber orientation is evaluated using the advanced pARD‐RSC fiber orientation tensor evaluation model, via the one‐way weakly‐coupled flow/orientation analysis formulation. Computed results show the fiber orientation state on the entire cross‐section of a deposited bead, which yields a clear view of how the material anisotropy is affected by the locally varied fiber orientation. The 3D‐flow prediction proves that the transverse directional fiber alignments are in high degree of similarity as compared to the over‐predicted results from the simplified 2D planar flows. In addition, the 3D‐model results exhibit a more favorable agreement with the reported experimental data than that yielded by the conventional 2D models.

An orientation corrected shaking method for the microstructure generation of short fiber-reinforced composites with almost planar fiber orientation

We present an algorithm for generating short fiber-reinforced microstructures with almost planar fiber orientation. The orientation corrected shaking (OCS) method achieves a high accuracy regarding the volume fraction, fiber length distribution and fiber orientation state. Additionally, the algorithm is capable of generating microstructures for industrial materials, e.g., for a PA66GF35 material with a volume fraction of 19.3% and an aspect ratio of 33. For typical manufacturing processes, short fiber-reinforced composites show a mainly planar fiber arrangement. Therefore, we extend the two-step shaking algorithm of Li et al. [J. Ind. Text. 51(1), pp. 506–530, 2022] for a user-selected rectangular size of the unit cell and periodic boundary conditions. Additionally, the hidden closure structure of the algorithm is uncovered and a precise realization of the fiber orientation state achieved. We examine the representative volume element size for the OCS method, observing representative errors below 2% even for unit cells with edge lengths smaller than the mean fiber length. Additionally, the influence of different closure approximations on the stiffness is investigated. When applied to an industrial PA66GF35 material with sandwich structure, the OCS method demonstrates differences below 2% and 9% for the computed directional Young’s moduli E1 and E2 compared to experimental data.

Numerical modelling on polymer composites prepared via large area extrusion-deposition additive manufacturing: fibre orientation, material inhomogeneity, and thermal-mechanical responses during material loading process

ABSTRACT The flow-induced fibre orientation formed during polymer extrusions causes the composite to exhibit non-homogeneous thermal-mechanical behaviours during Large Area extrusion-deposition Additive Manufacturing (LAAM) processes. This study numerically evaluates the fibre orientation state of a 20 wt.% short carbon fibre reinforced polyethylenimine fabricated by LAAM. The fibre orientation state of the solidified deposited bead is determined by a fully coupled flow/orientation simulation approach. The material properties of deposited composites are computed by assuming that the deposited bead has heterogeneous regions with varying local fibre orientation states. A finite element simulation is performed to model the LAAM process of a thin-wall structure, where the predicted inhomogeneous material properties are employed. Computed results show notable differences between simulations performed by employing homogenous properties and those obtained using heterogeneous properties. The bead-direction tensile stress contours computed under the heterogeneous assumption are comparable to experimental data in the literature, supporting our numerical approach.

A strain rate dependent and anisotropic failure material model for short fiber reinforced plastics based on energy density accounting for local fiber orientation

A failure model for SFRP for FEM simulations is developed to describe the strain rate dependency, the influence of the local fiber orientation and of the stress state on the failure behavior. The material is considered as a continuum while internally calculating the micro-mechanics analytically. The described micro-mechanics are based on experimental observations and on analyzation with numerical studies. In particular the strain rate dependent delamination of fibers and matrix is incorporated in the model. The distortion energy density is defined as the driving value for failure and estimated by the model. This is achieved with the analytic solution by Eshelby for the stress field in the matrix and by introducing an additional phase for the plasticly deformed volume. The validation on characterization specimens as well as component test demonstrates that the influence of strain rate, fiber orientation, and stress state on the failure behavior can be described with only one material parameter, the critical distortion energy density.

Computational modeling of fiber orientation during 3D-concrete-printing

During 3D-printing of fiber-reinforced concrete, fibers tend to align with the printing direction due to strong shearing deformation of the material, allowing for the controlled production of components with desired fiber orientation states. The accurate prediction of the fiber orientation state in printed components poses a major challenge due to the large number of processing and material parameters involved and due to the complex mechanisms of flow and fiber reorientation during printing. This contribution presents a novel incorporation of the Folgar–Tucker fiber orientation model within a fluid dynamics framework based on the Particle Finite Element Method for simulations of the fiber orientation evolution during 3D-concrete-printing. The fiber orientation state is represented using a second-order orientation tensor, which is coupled with a new anisotropic Bingham constitutive model used for the viscous fiber-concrete mixture to account for the effect of fiber orientation on the velocity field. Further, the orientation distribution function is reconstructed from the second-order orientation tensor, following the maximum entropy method for a more convenient interpretation of the results. The model is validated by comparing the simulated orientation numbers of a 3D-printed concrete layer for different extrusion nozzle diameters with experimental values from the literature. Several parametric studies are performed to examine the flow and fiber reorientation mechanisms and the influence of process parameters on the fiber orientation state in printed components. Stronger fiber alignment in the printing direction is obtained for higher printing speeds or smaller extrusion nozzles, associated with higher shear stresses developing in the extrusion nozzle.

Unified mean-field modeling of viscous short-fiber suspensions and solid short-fiber reinforced composites

Mean-field homogenization is an established and computationally efficient method estimating the effective linear elastic behavior of composites. In view of short-fiber reinforced materials, it is important to homogenize consistently during process simulation. This paper aims to comprehensively reflect and expand the basics of mean-field homogenization of anisotropic linear viscous properties and to show the parallelism to the anisotropic linear elastic properties. In particular, the Hill–Mandel condition, which is generally independent of a specific material behavior, is revisited in the context of boundary conditions for viscous suspensions. This study is limited to isothermal conditions, linear viscous and incompressible fiber suspensions and to linear elastic solid composites, both of which consisting of isotropic phases with phase-wise constant properties. In the context of homogenization of viscous properties, the fibers are considered as rigid bodies. Based on a chosen fiber orientation state, different mean-field models are compared with each other, all of which are formulated with respect to orientation averaging. Within a consistent mean-field modeling for both fluid suspensions and solid composites, all considered methods can be recommended to be applied for fiber volume fractions up to 10%. With respect to larger, industrial-relevant, fiber volume fractions up to 20%, the (two-step) Mori–Tanaka model and the lower Hashin–Shtrikman bound are well suited.

非連続炭素繊維強化ポリアミド 6 における X 線回折像に基づく繊維配向状態指標と引張特性との関係

非連続炭素繊維強化ポリアミド 6 における X 線回折像に基づく繊維配向状態指標と引張特性との関係

Mechanisms of notch insensitivity in long-fiber discontinuous, prepreg platelet compression molded composites

The present treatise offers an investigation into the operative mechanisms of stress redistribution and notch insensitivity of the prepreg-based, long-fiber discontinuous composites with stochastic fiber orientation state manufactured via a compression molding process. Open-hole tensile behavior is examined to determine the source of notch insensitivity. Both experimental and simulation approaches reveal that local damage mechanisms result in stress redistribution and corresponding reduction in notch sensitivity as measured by the ratio of the notched to un-notched tensile strengths. The analysis showed that open-hole coupon fracture may occur in locations at or away from the hole, depending on the details of the stochastic meso-morphology and the notch size. It was also demonstrated that as the notch diameter is increased, the probability of fracture at the notch is increased. The experimentally observed notch insensitivity of the prepreg platelet composite was reproduced in the numerical simulations.

Bayesian inference of fiber orientation and polymer properties in short fiber-reinforced polymer composites

We present a Bayesian methodology to infer the elastic modulus of the constituent polymer and the fiber orientation state in a short-fiber reinforced polymer composite (SFRP). The properties are inversely determined using only a few experimental tests. Developing composite manufacturing digital twins for SFRP composite processes, including injection molding and extrusion deposition additive manufacturing (EDAM) requires extensive experimental material characterization. In particular, characterizing the composite mechanical properties is time consuming and therefore, micromechanics models are used to fully identify the elasticity tensor. Hence, the objective of this paper is to infer the fiber orientation and the effective polymer modulus and therefore, identify the elasticity tensor of the composite with minimal experimental tests. To that end, we develop a hierarchical Bayesian model coupled with a micromechanics model to infer the fiber orientation and the polymer elastic modulus simultaneously which we then use to estimate the composite elasticity tensor. We motivate and demonstrate the methodology for the EDAM process but the development is such that it is applicable to other SFRP composites processed via other methods. Our results demonstrate that the approach provides a reliable framework for the inference, with as few as three tensile tests, while accounting for epistemic and aleatory uncertainty. Posterior predictive checks show that the model is able to recreate the experimental data well. The ability of the Bayesian approach to calibrate the material properties and its associated uncertainties, make it a promising tool for enabling a probabilistic predictive framework for composites manufacturing digital twins.

Microstructure-guided deep material network for rapid nonlinear material modeling and uncertainty quantification

Modeling nonlinear materials with arbitrary microstructures and loading paths is crucial in structural analyses with heterogeneous materials with uncertainty. However, it is computationally prohibitive because (1) fine meshes are required to resolve the microstructures for nonlinear simulations, (2) enormous model evaluations are expected to simulate stochastic microstructures and the loading variabilities, and (3) nonlinear material models are generally expensive to solve. In this paper, we present the microstructure-guided deep material network (MgDMN), a deep-learning-based approach to model multi-phase materials and efficiently predict their mechanical response under virtually any loading paths and microstructure definitions considering plasticity. This work is built upon the earlier development of the deep material network (DMN) method for fast predictions of nonlinear homogenized responses of multi-phase materials using linear elastic training data for a predefined microstructure. We extend DMN to MgDMN for any microstructure definition by parameterizing the microstructure space, mapping a small set of DMNs to their respective microstructure parameters, and interpolating the DMNs to generate new models in the microstructure space. The proposed method achieves superb efficiency and accuracy since the interpolated DMNs do not need additional training to predict nonlinear behavior of any new microstructures. We demonstrate our approach via modeling and uncertainty quantification of short fiber reinforced polymer (SFRP) composites. We show that for this dual-phase material, only four base DMNs are needed to predict the nonlinear stress responses for any loading path given any fiber volume fraction, orientation states, and constituent properties as long as the combination is within the microstructure space enclosed by the base models. The accelerated modeling process enables complex structural simulations of heterogeneous materials and nonlinear stochastic analyses with uncertain microstructures, which are essential in computational materials engineering and multiscale modeling. Our research also draws insights into the impact of microstructure uncertainties on linear and nonlinear material behaviors.

Process-induced failure mode transition of compression molded discontinuous carbon fiber composites: From coupon to component level

Discontinuous carbon fiber composites have been reported to be damage tolerant materials with insensitivity to notches and defects. Meso-scale damage mechanisms and crack arresting are responsible for high apparent fracture toughness and pseudo-ductility. This work studies the effect of manufacturing and structure formation on the mechanical behavior of stochastic carbon fiber sheet molding compounds based on thermosetting prepreg platelets with a fiber length of 50 mm. The process–structure–property–performance relationship is analyzed by non-destructive characterization and mechanical bending tests on the component level. Model components of various preform and stack placement scenarios were compression molded to investigate different flow conditions, weld lines and artificially introduced defects. The experimental findings revealed a process-induced failure mode transition from pseudo-ductile to brittle failure behavior. Low-flow scenarios showed a highly non-linear response with large deflection values and high energy absorption. Higher in-mold material flow and weld lines caused brittle failure at significantly lower deflections with a considerable reduction of energy absorbing capacity. Increased material flow also reduced component stiffness and maximum load values. Weld lines exhibited major strength reduction compared to the pristine material configuration. Full-scale and high-resolution X-ray computed tomography scans revealed differences in local fiber orientation state, increased levels of fiber waviness and porosity, as well as asymmetric distribution of defects.

A numerical study on the predicted fiber orientation of large area extrusion deposition additive manufactured composites

AbstractThe recent‐emerging Large Area extrusion deposition Additive Manufacturing (LAAM) provides a low‐cost and high‐efficient alternative manufacturing approach for industries like automotive and aerospace. Fiber orientation information significantly determines the material performances of LAAM‐produced short fiber reinforced composites. Numerical studies have been performed to better understand the microstructural formation of the fiber orientation in deposited beads. The fully coupled flow/orientation analysis approach has been applied for LAAM deposition flow modeling. In contrast, the orientation analysis is still limited to the classic Folgar‐Tucker Isotropic Rotary Diffusion (IRD) model. This paper employs the advanced principle Anisotropic Rotary Diffusion Reduced Strain Closure (pARD‐RSC) orientation evaluation model to estimate the fiber alignment of the LAAM flows, which is firstly used in the simulations of extrusion deposition flows with free surface boundaries. The effects of constant parameters of the pARD‐RSC model are investigated. It is found that predicted fiber orientation results in the flow end are primarily sensitive to the value of the strain slip factor. The initial fiber orientation condition of the flow inlet is also studied. By comparing the computed results with experimentally reported data, it is found that the initial fiber orientation state of the flow inlet significantly impacts the fiber alignment patterns in the deposited beads.

Effect of Melt and Mold Temperature on Fiber Orientation during Flow in Injection Molding of Reinforced Plastics

Abstract Injection molding, a highly productive manufacturing process, is one of the most versatile production methods in plastic manufacturing industry. It is capable of producing intricate net shapes without requiring finishing treatment and with good dimensional accuracy. In injection molding of reinforced thermoplastics the properties of the final product highly depend on the state of fiber orientation. Tailoring the fiber orientation in the final product, in order to control the properties, is the basic motivation of this study. Among different parameters, which could affect the orientation patterns, this study is concerned on analyzing the effects of mold and melt temperature on the state of fiber orientation during flow. In contrast to the melt temperature, which has a limited range for variation, mold temperature provides wide range of possible input at different locations such that by revealing its effect it could become one of the most attractive parameters in controlling the properties of injection molded fiber reinforced thermoplastic products.